Benchmarks: Logloss

This notebook is all about benchmarking some R code used in this package.

Hardware / Software used:

• Intel i7-4600U
• Compilation flags for C/C++: -O2 -Wall $(DEBUGFLAG) -mtune=core2 (R’s defaults)
• Windows Server 2012 R2
• R 3.3.2 + Intel MKL

Libraries

library(data.table)

data.table 1.10.4
  The fastest way to learn (by data.table authors): https://www.datacamp.com/courses/data-analysis-the-data-table-way
  Documentation: ?data.table, example(data.table) and browseVignettes("data.table")
  Release notes, videos and slides: http://r-datatable.com

library(microbenchmark)
library(Rcpp)
library(ggplot2)
library(plotly)

Attaching package: <U+393C><U+3E31>plotly<U+393C><U+3E32>

The following object is masked from <U+393C><U+3E31>package:ggplot2<U+393C><U+3E32>:

    last_plot

The following object is masked from <U+393C><U+3E31>package:stats<U+393C><U+3E32>:

    filter

The following object is masked from <U+393C><U+3E31>package:graphics<U+393C><U+3E32>:

    layout

# Helper function to print data well in tables
print_well <- function(data, digits = 6) {
  
  # To milliseconds
  data <- data / 1000000
  
  # Sprintf helper
  sprintf_helper <- paste0("%.0", digits, "f")
  
  cat("| Min | 25% | 50% | 75% | Max | Mean |  \n| --: | --: | --: | --: | --: | --: |  \n| ", sprintf(sprintf_helper, min(data)), " | ", sprintf(sprintf_helper, quantile(data, probs = 0.25)), " | ", sprintf(sprintf_helper, median(data)), " | ", sprintf(sprintf_helper, quantile(data, probs = 0.75)), " | ", sprintf(sprintf_helper, max(data)), " | ", sprintf(sprintf_helper, mean(data)), " |  \n", sep = "")
  
  return(data)
  
}
# Test case function
# Arguments renamed to avoid recursive clash
test_case <- function(f, preds, labels, eps) {
  cat("Test case: ", do.call(f, list(preds = preds[1:50],
                                     labels = labels[1:50],
                                     eps = 1e-15)), "  \n", sep = "")
}

Benchmarking Clamped Vector to Logloss

For a 2-class vector of 1,000,000 observations:

• Vector A of length=(1000000)
• Vector B of length=(1000000) with 2 classes

A = [1, 2, 3, 4, ..., 1000000]
B = [0, 1, 1, 0, ...]

Get the following Vector C and D:

C = Clamped A by 1e-15
D = Mean of logloss(C, B)

Initialize data

# How many digits for benchmarking in milliseconds
my_digits <- 6L
# How many runs for benchmarking?
my_runs <- 1000L
# How many observations?
my_obs <- 1000000L
# Generate random data
set.seed(11111)
data <- runif(my_obs, 0, 1)
labels <- round(runif(my_obs, 0, 1), digits = 0)
# Background truth example (no clamping though)
data[1:5]

[1] 0.5014483 0.9702328 0.7876004 0.9022259 0.8141778

labels[1:5]

[1] 0 1 1 0 0

- (labels[1:5] * log(data[1:5]) + (1 - labels[1:5]) * log(1 - data[1:5]))

[1] 0.69604803 0.03021924 0.23876448 2.32509520 1.68296488

mean(- (labels[1:5] * log(data[1:5]) + (1 - labels[1:5]) * log(1 - data[1:5])))

[1] 0.9946184

Benchmarks

# ===== BLOCK 1 =====
faster1 <- function(preds, labels, eps = 1e-15) {
  x <- preds
  x[x < eps] <- eps
  x[x > (1 - eps)] <- 1 - eps
  return(-mean(labels * log(x) + (1 - labels) * log(1 - x)))
}
test_case(faster1, preds = data, labels = labels, eps = 1e-15)

Test case: 0.9837966

data1 <- print_well(microbenchmark(faster1(data, labels), times = my_runs)$time, digits = my_digits)

Min	25%	50%	75%	Max	Mean
98.510398	101.366932	102.792063	107.315779	199.486360	111.547776

# ===== BLOCK 2 =====
faster2 <- function(preds, labels, eps = 1e-15) {
  x <- pmin(pmax(preds, eps), 1 - eps)
  return(-mean(labels * log(x) + (1 - labels) * log(1 - x)))
}
test_case(faster2, preds = data, labels = labels, eps = 1e-15)

Test case: 0.9837966

data2 <- print_well(microbenchmark(faster2(data, labels), times = my_runs)$time, digits = my_digits)

Min	25%	50%	75%	Max	Mean
98.961620	103.473076	106.699103	118.782302	198.907793	120.656334

# ===== BLOCK 3 =====
faster3 <- function(preds, labels, eps = 1e-15) {
  x <- preds
  x[x < eps] <- eps
  x[x > (1 - eps)] <- 1 - eps
  return(-1/length(labels) * (sum(labels * log(x) + (1 - labels) * log(1 - x))))
}
test_case(faster3, preds = data, labels = labels, eps = 1e-15)

Test case: 0.9837966

data3 <- print_well(microbenchmark(faster3(data, labels), times = my_runs)$time, digits = my_digits)

Min	25%	50%	75%	Max	Mean
95.665459	99.602340	101.189218	104.431305	183.179657	105.827194

# ===== BLOCK 4 =====
faster4 <- function(preds, labels, eps = 1e-15) {
  x <- pmin(pmax(preds, eps), 1 - eps)
  return(-1/length(labels) * (sum(labels * log(x) + (1 - labels) * log(1 - x))))
}
test_case(faster4, preds = data, labels = labels, eps = 1e-15)

Test case: 0.9837966

data4 <- print_well(microbenchmark(faster4(data, labels), times = my_runs)$time, digits = my_digits)

Min	25%	50%	75%	Max	Mean
98.256468	102.299787	105.832582	121.494859	201.112203	121.317011

# ===== BLOCK 5 =====
cppFunction("double faster5(NumericVector preds, NumericVector labels, double eps) {
  NumericVector clamped = clamp(eps, preds, 1 - eps);
  NumericVector loggy = -1 * ((labels * log(clamped) + (1 - labels) * log(1 - clamped)));
  double logloss = mean(loggy);
  return logloss;
}")
test_case(faster5, preds = data, labels = labels, eps = 1e-15)

Test case: 0.9837966

data5 <- print_well(microbenchmark(faster5(data, labels, eps = 1e-15), times = my_runs)$time, digits = my_digits)

Min	25%	50%	75%	Max	Mean
78.355197	79.850368	82.443752	86.616981	150.678771	83.917317

# ===== BLOCK 6 =====
cppFunction("double faster6(NumericVector preds, NumericVector labels, double eps) {
  NumericVector clamped = clamp(eps, preds, 1 - eps);
  NumericVector loggy = -1 * ((labels * log(clamped) + (1 - labels) * log(1 - clamped)));
  double logloss = sum(loggy)/loggy.size();
  return logloss;
}")
test_case(faster6, preds = data, labels = labels, eps = 1e-15)

Test case: 0.9837966

data6 <- print_well(microbenchmark(faster6(data, labels, eps = 1e-15), times = my_runs)$time, digits = my_digits)

Min	25%	50%	75%	Max	Mean
77.012176	78.687150	81.050362	85.269969	163.344910	82.639045

# ===== BLOCK 7 =====
faster7 <- function(preds, labels, eps = 1e-15) {
  x <- pmin(pmax(preds, eps), 1 - eps)
  return(-1/length(labels) * sum(log((1 - labels) + (2 * labels - 1) * x)))
}
test_case(faster7, preds = data, labels = labels, eps = 1e-15)

Test case: 0.9837966

data7 <- print_well(microbenchmark(faster7(data, labels, eps = 1e-15), times = my_runs)$time, digits = my_digits)

Min	25%	50%	75%	Max	Mean
60.741585	64.389943	66.863298	71.798132	153.880658	78.753778

# ===== BLOCK 8 =====
cppFunction("double faster8(NumericVector preds, NumericVector labels, double eps) {
  int label_size = labels.size();
  NumericVector clamped(label_size);
  clamped = clamp(eps, preds, 1 - eps);
  NumericVector loggy(label_size);
  loggy = -log((1 - labels) + ((2 * labels - 1) * clamped));
  double logloss = sum(loggy) / label_size;
  return logloss;
}")
test_case(faster8, preds = data, labels = labels, eps = 1e-15)

Test case: 0.9837966

data8 <- print_well(microbenchmark(faster8(data, labels, eps = 1e-15), times = my_runs)$time, digits = my_digits)

Min	25%	50%	75%	Max	Mean
51.169755	51.979825	53.973830	58.375617	124.569496	55.660620

Summary Results

data_time <- data.table(rbindlist(list(data.frame(Time = data1, Bench = "faster1"),
                                       data.frame(Time = data2, Bench = "faster2"),
                                       data.frame(Time = data3, Bench = "faster3"),
                                       data.frame(Time = data4, Bench = "faster4"),
                                       data.frame(Time = data5, Bench = "faster5"),
                                       data.frame(Time = data6, Bench = "faster6"),
                                       data.frame(Time = data7, Bench = "faster7"),
                                       data.frame(Time = data8, Bench = "faster8"))))
data_time <- data_time[, t_mean := mean(Time), by = Bench]
data_time <- data_time[, t_median := median(Time), by = Bench]
data_time$Benchs <- data_time$Bench 
levels(data_time$Benchs) <- paste0("faster", 1:8, "= [", sprintf(paste0("%.0", my_digits, "f"), data_time[, list(min(Time)), by = Bench]$V1), ", ", sprintf(paste0("%.0", my_digits, "f"), data_time[, list(max(Time)), by = Bench]$V1), "], mean=", sprintf(paste0("%.0", my_digits, "f"), data_time[, list(mean(Time)), by = Bench]$V1), ", median=", sprintf(paste0("%.0", my_digits, "f"), data_time[, list(median(Time)), by = Bench]$V1))
my_time <- data_time[, list(min(Time), quantile(Time, probs = 0.25), median(Time), quantile(Time, probs = 0.75), max(Time), mean(Time)), by = Bench]
colnames(my_time) <- c("Function", "Min", "25%", "50%", "75%", "Max", "Mean")
my_time <- my_time[order(Mean, decreasing = FALSE), ]
print(my_time, digits = 6)

Plot Results

ggplotly(ggplot(data = data_time, aes(x = Time)) + geom_histogram(aes(y = ..density..), bins = 20, color = "darkblue", fill = "lightblue") + facet_wrap(~ Benchs, ncol = 2) + geom_vline(aes(xintercept = t_mean), color = "blue", linetype = "dashed", size = 2) + geom_vline(aes(xintercept = t_median), color = "red", linetype = "dashed", size = 2) + labs(x = "Time (Milliseconds)", y = "Density") + theme_bw())

ggplotly(ggplot(data = data_time[, .(Time, Bench)], aes(x = Time, y = ..count.., fill = Bench)) + geom_histogram(aes(y = ..density..), bins = 100, position = "fill") + labs(x = "Time (Milliseconds)", y = "Density") + theme_bw())

ggplotly(ggplot(data = data_time[, .(Time, Bench)], aes(x = Time, y = ..count.., fill = Bench)) + geom_density(position = "fill") + labs(x = "Time (Milliseconds)", y = "Density") + theme_bw())

data_time$MilObs <- (1000 / data_time$Time) * my_obs / 1000000
ggplotly(ggplot(data_time[, .(Bench, MilObs)], aes(x = Bench, y = MilObs, fill = Bench)) + geom_boxplot() + labs(x = "Benchmark", y = "Throughput (Million Obs./s)") + theme_bw())

Scaling Benchmarks

Benchmarker <- function(f, size, runs, digits, name) {
  
  data_runs <- list()
  
  for (i in 1:length(size)) {
    set.seed(11111)
    data <- runif(size[i], 0, 1)
    labels <- round(runif(size[i], 0, 1), digits = 0)
    cat("  \n  \n## ", name, " run: ",format(size[i], big.mark = ",", scientific = FALSE), " samples (", format(runs[i], big.mark = ",", scientific = FALSE), " times)  \n  \n", sep = "")
    test_case(f, preds = data, labels = labels, eps = 1e-15)
    cat("  \n")
    data_runs[[i]] <- print_well(microbenchmark(f(data, labels, eps = 1e-15), times = runs[i])$time, digits = digits)
    data_runs[[i]] <- data.table(Bench = as.factor(paste0("[", i, "] ", format(size[i], big.mark = ",", scientific = FALSE))), Function = as.factor(name), Time = data_runs[[i]])
    gc(verbose = FALSE)
  }
  
  return(data_runs)
  
}
bench_size <- c(100, 1000, 10000, 100000, 1000000, 10000000, 100000000)
bench_runs <- c(10000, 5000, 1000, 500, 100, 50, 10)

run1 <- Benchmarker(faster7, bench_size, bench_runs, my_digits, "Pure R")

Pure R run: 100 samples (10,000 times)

Test case: 1.13218

Min	25%	50%	75%	Max	Mean
0.020527	0.022808	0.023569	0.034972	4.309224	0.029422

Pure R run: 1,000 samples (5,000 times)

Test case: 1.193473

Min	25%	50%	75%	Max	Mean
0.061202	0.068805	0.069945	0.076407	3.311367	0.077917

Pure R run: 10,000 samples (1,000 times)

Test case: 1.159039

Min	25%	50%	75%	Max	Mean
0.481632	0.532571	0.537513	0.618862	4.236619	0.605984

Pure R run: 100,000 samples (500 times)

Test case: 0.9539782

Min	25%	50%	75%	Max	Mean
4.980164	5.626111	5.798597	6.117342	84.356026	6.520741

Pure R run: 1,000,000 samples (100 times)

Test case: 0.9837966

Min	25%	50%	75%	Max	Mean
60.215477	64.248722	65.580910	67.840913	151.788769	73.396825

Pure R run: 10,000,000 samples (50 times)

Test case: 0.9312716

Min	25%	50%	75%	Max	Mean
604.348530	632.697758	649.104247	701.033229	776.059097	665.486103

Pure R run: 100,000,000 samples (10 times)

Test case: 1.413474

Min	25%	50%	75%	Max	Mean
6321.118923	6364.084769	6535.476782	6613.934425	6681.649989	6503.505692

run2 <- Benchmarker(faster8, bench_size, bench_runs, my_digits, "Rcpp")

Rcpp run: 100 samples (10,000 times)

Test case: 1.13218

Min	25%	50%	75%	Max	Mean
0.005702	0.006082	0.006462	0.006843	0.107199	0.007003

Rcpp run: 1,000 samples (5,000 times)

Test case: 1.193473

Min	25%	50%	75%	Max	Mean
0.045996	0.049418	0.050938	0.052079	0.137229	0.052078

Rcpp run: 10,000 samples (1,000 times)

Test case: 1.159039

Min	25%	50%	75%	Max	Mean
0.460725	0.486575	0.511853	0.555664	2.341640	0.547915

Rcpp run: 100,000 samples (500 times)

Test case: 0.9539782

Min	25%	50%	75%	Max	Mean
4.611053	5.099052	5.235616	5.437088	8.441685	5.341539

Rcpp run: 1,000,000 samples (100 times)

Test case: 0.9837966

Min	25%	50%	75%	Max	Mean
47.781602	51.192848	51.665453	52.588518	118.033053	53.538399

Rcpp run: 10,000,000 samples (50 times)

Test case: 0.9312716

Min	25%	50%	75%	Max	Mean
515.161353	528.701044	554.947169	566.630370	628.325622	549.245088

Rcpp run: 100,000,000 samples (10 times)

Test case: 1.413474

Min	25%	50%	75%	Max	Mean
5351.091904	5365.159034	5511.260205	5548.570193	5586.359344	5469.415267

Scaling Results

run1_all <- rbindlist(run1)
run2_all <- rbindlist(run2)
run_all <- rbind(run1_all, run2_all)
run_all$Repeats <- rep(inverse.rle(list(lengths = bench_runs, values = bench_size)), 2)
run_all$MilObs <- (1000 / run_all$Time) * run_all$Repeats / 1000000
run_time <- run_all[, list(quantile(Time, probs = 0.05), median(Time), quantile(Time, probs = 0.95), mean(Time)), by = list(Function, Bench)]
colnames(run_time) <- c("Function", "Benchmark", "5%", "50%", "95%", "Mean")
run_time$`Mil.Obs/s` <- (1000 / run_time$Mean) * bench_size / 1000000
run_time$`5%` <- format(run_time$`5%`, digits = 6, scientific = FALSE)
run_time$`50%` <- format(run_time$`50%`, digits = 6, scientific = FALSE)
run_time$`95%` <- format(run_time$`95%`, digits = 6, scientific = FALSE)
run_time$Mean <- format(run_time$Mean, digits = 6, scientific = FALSE)
run_time$`Mil.Obs/s` <- format(run_time$`Mil.Obs/s`, digits = 6, scientific = FALSE)
print(run_time[1:(nrow(run_time) / 2)])

print(run_time[(nrow(run_time) / 2 + 1):nrow(run_time)])

ggplot(run_all, aes(x = Bench, y = Time, color = Function, fill = Bench)) + geom_boxplot() + scale_y_log10(labels = scales::comma, breaks = c(0.01, 0.1, 1, 10, 100, 1000, 10000)) + stat_summary(fun.y = mean, geom = "line", aes(group = Function)) + stat_summary(fun.y = mean, geom = "point", aes(group = Function)) + labs(x = "Benchmark", y = "Time (Milliseconds)") + theme_bw()

ggplot(run_all, aes(x = Bench, y = MilObs, color = Function, fill = Bench)) + geom_boxplot() + scale_y_log10(labels = scales::comma, breaks = c(1, 2.5, 5, 7.5, 10, 12.5, 15, 17.5, 20, 22.5, 25), limits = c(1, NA)) + stat_summary(fun.y = mean, geom = "line", aes(group = Function)) + stat_summary(fun.y = mean, geom = "point", aes(group = Function)) + labs(x = "Benchmark", y = "Throughput (Million Obs./s)") + theme_bw()

ggplot(data = run_all, aes(x = MilObs, color = Function, fill = Function, group = Function)) + coord_flip() + stat_ecdf(aes(ymin = ..y.., ymax = 1), alpha = 0.5, geom = "ribbon") + stat_ecdf(geom = "line", size = 2, alpha = 0.75, pad = FALSE) + labs(x = "Throughput (Million Obs./s)", y = "Percentile") + facet_wrap(~ Bench, dir = "h", ncol = 2, scales = "free") + theme_bw()